MinT - Best Known (219−107, 219, s)-Nets in Base 4

Best Known (219−107, 219, s)-Nets in Base 4

(219−107, 219, 130)-Net over F₄ — Constructive and digital

Digital (112, 219, 130)-net over F₄, using

t-expansion [i] based on digital (105, 219, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(219−107, 219, 167)-Net over F₄ — Digital

Digital (112, 219, 167)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−107, 219, 2012)-Net in Base 4 — Upper bound on s

There is no (112, 219, 2013)-net in base 4, because

1 times m-reduction [i] would yield (112, 218, 2013)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 177936 086131 781929 486602 162722 665369 012103 559178 166244 309633 123331 710057 161392 773259 899690 233178 773213 318849 561098 847733 207334 501960 > 4²¹⁸ [i]